A company manufactures three products: A, B and C by using three resources each unit of product X takes six man-hour twenty hour of machine capacity 2 cubic meter of storage place .
Similarly, one unit of product B takes ten man hour s and four machine hour on two cubic meter of storage place and that of each unit of product C is ten man hours, twelve machine hours and two cubic meter of storage place.
The profit contribution of products A,B and C are eight, ten and twelve birr respectively.
Formulate the linear programming problem calculate optimum quantities of products slacks and total profit and also conduct sensitivity analysis accordingly using simplest method ?